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<h3 class="heading"><span class="type">Paragraph</span></h3>
<p>For a given <span class="process-math">\(n\text{,}\)</span> we get a solution <span class="process-math">\(T_n(t)\text{,}\)</span> which solves</p>
<div class="displaymath process-math" data-contains-math-knowls="">
\begin{equation*}
\begin{aligned}
&amp;T'(t)+\alpha^2\lambda_n T ~~= ~~T'(t)+ \alpha^2 \frac{n^2\pi^2}{L^2} T~~ = ~0&amp;\nonumber\\
&amp;T_n(t)=C_n\cdot\exp\left[-\left(\frac{n\pi\alpha}{L}\right)^2t\right],&amp;\label{Tsol}
\end{aligned}
\end{equation*}
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<p class="continuation">where <span class="process-math">\(C_n\)</span> are arbitrary constants, <span class="process-math">\(n={1},2,3,\cdots\text{.}\)</span></p>
<span class="incontext"><a href="sec7_7.html#p-406" class="internal">in-context</a></span>
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